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Sat 20 Sep, 2003 08:10 pm
I've been too lazy to solve the following problem myself since it'll involve me writing a program.
Problem:
Suppose you have two loans. With Loan A, you owe $2000 with interest rate at 7.25%. You owe $7000 in Loan B with interest rate at 5.75%. Suppose there is no minimum payment each month, and you decided to put down $1000 on either one of the loans each month. What's the minimum amount that you'll pay in total? What combination of payment would get you to pay as little on interest as possible?
Interest is accrued daily. For instance, to determine the amount of interest that'll be added to the principal today in Loan A, it would be: (2000 * 0.0725) / 365 = $0.40, so tommorow I'll owe $2000.40.
(For simplificity, you can assume it's accrued monthly.)
My friend argues that you should pay off the high interest rate loan first, I believe there's a combination of payments that'll be the best. (For example, in month 1 put $1000 to Loan B, month 2 put $1000 in Loan B, and then Loan A, and so on.)
I believe your friend is correct Blackie. These are 2 distinct and seperate loans with different interest rates. The minimum total will always be based on the highest interest rate loan being paid in full first.
fishin' wrote:I believe your friend is correct Blackie. These are 2 distinct and seperate loans with different interest rates. The minimum total will always be based on the highest interest rate loan being paid in full first.
That's the same argument he made, but I don't believe it since I haven't been presented with a formal proof.
Well, sorry but I'm not going to generate the 20,000 or so possible proofs for the scenario you presented.
Since your main question was "What combination of payment would get you to pay as little on interest as possible?" the solution would seem to be pretty intuitave.
Any time you make a payment on the lower rate loan you will accrue interest on the higher rate loan and that can never result in the minimum total.
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